alias NumType = Int32 | Int64 | UInt32 | UInt64

def trial_division(n : NumType)
  factors = [] of NumType
  check = ->(p: NumType) {
    q, r = n.divmod(p)
    while r.zero?
      factors << p
      n = q
      q, r = n.divmod(p)
    end
  }

  check.call(2)
  check.call(3)
  p = 5
  while p * p <= n
    check.call(p)
    p += 2
    check.call(p)
    p += 4
  end
  factors << n if n > 1
  factors
end

puts trial_division(600851475143).max